derivative f(x)=\sqrt[7]{x^6}

Lösung

ableitung von

f (x) = 7 x^{6}

\frac{6 x ^{5}}{7 ( x ^{6} ) ^{\frac{6}{7}}}

Schritte zur Lösung

\frac{d}{d x} (7 x^{6})

Wende die Kettenregel an:

\frac{1}{7 ( x ^{6} ) ^{\frac{6}{7}}} \frac{d}{d x} (x^{6})

= \frac{1}{7 ( x ^{6} ) ^{\frac{6}{7}}} \frac{d}{d x} (x^{6})

\frac{d}{d x} (x^{6}) = 6 x^{5}

= \frac{1}{7 ( x ^{6} ) ^{\frac{6}{7}}} \cdot 6 x^{5}

Vereinfache

\frac{1}{7 ( x ^{6} ) ^{\frac{6}{7}}} \cdot 6 x^{5} : \frac{6 x ^{5}}{7 ( x ^{6} ) ^{\frac{6}{7}}}

= \frac{6 x ^{5}}{7 ( x ^{6} ) ^{\frac{6}{7}}}

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